From EP 0 517 951 B1 there is known a traveller assembly in which a guide member unit can be attached to a basic body by means of a plurality of fastening screws. The fastening screws traverse the guide member unit and are screwed into respective threaded holes in the basic body with a threaded portion thereof. Within the guide member unit associated to at least one of the fastening screws there is provided an advancing mechanism by means of which the guide member unit is supported on the respective fastening screw and is movable towards a raceway under the generation of an advancing force. With such a traveller assembly there exists a problem that after once having determined a position of the threaded openings for the fastening screws and having provided the threaded openings at these positions the guide member unit can only be displaced with respect to the basic body for providing the advancing movement; the guide member unit is fixed to the basic body in a defined position against other movements.